Question

A body moves in straight line with velocity $v_1$ for ${\left(\frac{1}{3}\right)}^{rd}$ of time and for remaining time with $v_2$. Find the average velocity of body.

• A. $\frac{v_1}{3}+\frac{2v_2}{3}$
• B. $\frac{v_1}{3}+\frac{v_2}{3}$
• C. $\frac{2v_1}{3}+\frac{v_2}{3}$
• D. $v_1+\frac{2v_2}{3}$

Answer 1

The correct option is A $\frac{v_1}{3}+\frac{2v_2}{3}$

As we know that, average velocity of the body is given by
$\frac{\text{Total displacement}}{\text{Total time}}$
$\Rightarrow v_{\text{avg}}=\frac{v_1\left(\frac{t}{3}\right)+v_2\left(\frac{2t}{3}\right)}{t}=\frac{v_1}{3}+\frac{2v_2}{3}$